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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 116886.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 116886.c1 | 116886b6 | \([1, 1, 0, -9575216, 11400258324]\) | \(54804145548726848737/637608031452\) | \(1129561521807136572\) | \([2]\) | \(5242880\) | \(2.6149\) | |
| 116886.c2 | 116886b4 | \([1, 1, 0, -2143396, -1208679776]\) | \(614716917569296417/19093020912\) | \(33824451219883632\) | \([2]\) | \(2621440\) | \(2.2683\) | |
| 116886.c3 | 116886b3 | \([1, 1, 0, -613956, 168215040]\) | \(14447092394873377/1439452851984\) | \(2550078533913627024\) | \([2, 2]\) | \(2621440\) | \(2.2683\) | |
| 116886.c4 | 116886b2 | \([1, 1, 0, -139636, -17244080]\) | \(169967019783457/26337394944\) | \(46658301724387584\) | \([2, 2]\) | \(1310720\) | \(1.9218\) | |
| 116886.c5 | 116886b1 | \([1, 1, 0, 15244, -1477296]\) | \(221115865823/664731648\) | \(-1177612663062528\) | \([2]\) | \(655360\) | \(1.5752\) | \(\Gamma_0(N)\)-optimal |
| 116886.c6 | 116886b5 | \([1, 1, 0, 758184, 815041836]\) | \(27207619911317663/177609314617308\) | \(-314645735012752777788\) | \([2]\) | \(5242880\) | \(2.6149\) |
Rank
sage: E.rank()
The elliptic curves in class 116886.c have rank \(0\).
Complex multiplication
The elliptic curves in class 116886.c do not have complex multiplication.Modular form 116886.2.a.c
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 8 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 2 & 4 & 1 & 2 & 4 & 2 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 8 & 4 & 4 & 2 & 1 & 8 \\ 4 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
